Correlation and Causation Review 1 Two types of correlational study When same items have values on two score variables correlate the scores on one with the scores on the other Measure degree of correlation in terms of Pearson coefficient r Predict value on one variable from that on the other using the regression line y ax b When one nominal variable divides a population into two or more sub populations compare the two populations on another score variable in terms of their central tendencies If the means are different predict the value on the score variable depending on the value of the nominal variable Review 2 In both types of correlational studies one commonly makes inferences from a sample to an actual total population Does what is found in the sample apply to the actual population Addressed in terms of statistical significance Is the result in the sample one that would be unlikely to happen by chance if there weren t a correlation or a difference in the actual population The p value specifies the likelihood of the result in the sample happening by chance in drawing the sample p 05 indicates there is less than 5 chance of the result happening by chance 1 Review 3 In testing a claim about differences in the means of two sub populations one tests the null hypothesis There is no difference in the means The strategy is to try to reject the null hypothesis in terms of the results in the sample If the differences in means in the sample are statistically significant at a choosen level one infers that the null hypothesis is false Therefore the means differ in the real populations If the differences in means in the sample are not statistically signfiicant at the choosen level one cannot reject the null hypothesis Whatever differences there might be they will not have been detected Review 4 Two types of errors Type 1 error concluding that there is a difference between the two groups in the population when there is no difference Type 2 error concluding that there is no detectable difference between the two groups in the population when there is a difference To reduce Type 1 error demand a higher p value before accepting that there really is a difference To reduce Type 2 error use a larger sample size Which is more likely to produce a statistically significant difference if there really is a difference in the two groups The Logic of Correlational Research To confirm or falsify a correlational claim based on a sample we use modus tollens The first premise in each case though is different Confirming a correlational claim If there is no difference between means in the population then there will not be a statistically significant difference in my sample There is a statistically significant difference in means in my sample There is a difference between means in the population We pick the level of significance in the first premise according to how great a risk of error we can accept 2 Avoid Confirming the Consequence What about this argument If there is a difference between means in the population then there will be a statistically significant difference in my sample There is a statistically significant difference in means in my sample There is a difference between means in the population XXX It is INVALID The Logic of Correlational Research 2 Falsifying a correlational claim If there is a detectable difference between means in the population then there will be a statistically significant difference in my sample There is no statistically significant difference in means in my sample There is no detectable difference between means in the population The truth of the first premise depends upon using a large enough sample Quest for finding causes When something happens we ask Why We want to know what caused the event Why are we interested in causes Knowing the causes frequently provides understanding Knowing causes empowers us to intervene These two tend to go together Why do these barrels produce better beer Learning the reason is more hops provides understanding And a procedure for making better beer How does HIV cause AIDS Knowing about protease inhibitors explains And tells us a good place to intervene 3 What is a cause The roots of appeal of causation lie in our doing something to produce and effect We want to move a rock so we push it We want to see a friend so we walk to her apartment We want to stay warm so we put on a jacket Independent of our own action a cause is something which brings about or increases the likelihood of an effect The cause of the explosion was the spark from the generator Correlation and Causation A major reason people are interested in correlations is that they might be indicative of causation Correlations per se only allow you to predict The correlation of unprotected sex with having a baby nine months later allows you to predict that if you engage in unprotected sex you are more likely to have a baby nine months later Causation tells you how to change the effect Knowing that unprotected sex causes increases the likelihood of having a baby nine months later allows you to take action to have or not have a baby Correlations Point to Causation Statistical relations between variables that exceed what is statistically expected are typically due to causal relations Although not necessary direct causal relations Examples Consumption of red wine and reduced heart attacks Book that have a green cover and books that do not selling many copies Good study habits and good grades 4 Correlation Symmetrical Causation Asymmetrical Being run into in a traffic accident might be a cause for the big dent in your car Having a big dent in your car is correlated with having a car accident but it is not the cause of having a car accident Causation is directional correlation is symmetrical So when correlation points to causation we still need to establish the direction Problem of Directionality Does watching violence on TV result in aggressive behavior Or do the factors that generate aggressive behavior cause children to watch more violence on TV Causal Loops Sometimes X causes Y and then Y causes more X The causation here is still directional but works in both directions Back pain may be the cause of a person limping but walking with a limp may cause further back pain 5 Snoring and Obesity There is a positive correlation between obesity and snoring Does obesity cause increased snoring Yes via fat buildup in the back of the throat But fat build up also causes sleep apnea Sleeper stops